We introduce Four Q, a high-security, high-performance elliptic curve that targets the 128-bit
security level. At the highest arithmetic level, cryptographic scalar multiplications on Four Q …

We select a set of elliptic curves for cryptography and analyze our selection from a
performance and security perspective. This analysis complements recent curve proposals …

Isogenies are the morphisms between elliptic curves and are, accordingly, a topic of interest
in the subject. As such, they have been well studied, and have been used in several …

We propose a new unified point compression format for Edwards, Twisted Edwards and
Montgomery curves over large-characteristic fields, which effectively divides the curve's …

An analysis is made of the properties and conditions for the existence of 3-and 5-isogenies
of complete and quadratic supersingular Edwards curves. For the encapsulation of keys …

CSIDH is an isogeny-based key exchange protocol proposed by Castryck et al. in 2018. It is
based on the ideal class group action on F p-isomorphism classes of Montgomery curves …

The analysis of the 2-isogeny existence conditions of generalized Edwards form curves over
a prime field, including complete, quadratic, and twisted Edwards curves, is presented. An …

In this paper, we give a survey and discuss new developments and computational results for
a high order accurate numerical boundary condition based on finite difference methods for …

In this paper we look at three families of elliptic curves with rational 3-torsion over a finite
field. These families include Hessian curves, twisted Hessian curves, and a new family we …

Edwards' elliptic curve form is popular in modern cryptographic implementations thanks to
their fast, strongly unified addition formulas. Twisted Edwards curves with a= &# 8722; 1 are …